13(x+2)=2/3x+4

Solution for 13(x+2)=2/3x+4 equation:

13(x+2)=2/3x+4

We move all terms to the left:

13(x+2)-(2/3x+4)=0


Domain of the equation: 3x+4)!=0

x∈R


We multiply parentheses

13x-(2/3x+4)+26=0

We get rid of parentheses

13x-2/3x-4+26=0

We multiply all the terms by the denominator


13x*3x-4*3x+26*3x-2=0

Wy multiply elements

39x^2-12x+78x-2=0

We add all the numbers together, and all the variables

39x^2+66x-2=0

a = 39; b = 66; c = -2;
Δ = b2-4ac
Δ = 662-4·39·(-2)
Δ = 4668
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4668}=\sqrt{4*1167}=\sqrt{4}*\sqrt{1167}=2\sqrt{1167}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1167}}{2*39}=\frac{-66-2\sqrt{1167}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1167}}{2*39}=\frac{-66+2\sqrt{1167}}{78}
$